partial update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / etc / head / path_head_structure.etc

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/path_head_structure.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/path_head_structure.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/path_head_structure.etc
@@ -0,0 +1,39 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "delayed_updating/syntax/path_head_depth.ma".
+include "delayed_updating/syntax/path_structure_labels.ma".
+
+(* HEAD FOR PATH ************************************************************)
+
+(* Constructions with structure *********************************************)
+
+lemma path_head_structure_height (p) (n):
+      ⊗↳[n]p = ↳[n+♯↳[n]p]⊗p.
+#p elim p -p //
+#l #p #IH #n @(nat_ind_succ … n) -n //
+#n #_ cases l [ #k ]
+[ <height_d_dx <structure_d_dx //
+| <structure_m_dx //
+| <structure_L_dx //
+| <height_A_dx <structure_A_dx <nplus_succ_sn <path_head_A_dx //
+| <height_S_dx <structure_S_dx <nplus_succ_sn <path_head_S_dx //
+]
+qed.
+
+lemma path_head_structure_depth (p) (n):
+      ⊗↳[n]p = ↳[♭↳[n]p]⊗p.
+#p #n
+<path_head_depth //
+qed.